Are people who have been given the information that they're using a placebo trully convinced of that or do they just have a mental barrier preventing them from further acknowledging it and just resign to respond: "yeah, I know it's just a placebo"
A true test of placebo effect must be one where you'd have a group who does not use a placebo, and a group that does! But then how would you study it blind?
Maybe a better (and possible) test would be to give everyone the placebo, but divide participants into three groups. One would be told they're given a real treatment, the other would be told they're given a placebo for the real treatment, and the third would be told they're given a sugar pill for no specific reason other than to see what happens.
1+2 would then tell you about whether or not knowing if you're getting a real treatment or placebo matters; 2+3 would tell you how much knowing you have a problem to treat in the first place matters.